Let $A$ be a matrix given by $A=[a_{ij}]_{3\times3}$, $a_{ij}=i+j$, then

Match List-I with List-II

List-I	List-II
(A) Number of the elements in $A$	(I) 3
(B) Sum of the diagonal elements	(II) 9
(C) $a_{31}+a_{32}-a_{33}$	(III) -1
(D) Cofactor of $a_{13}$	(IV) 12

Choose the correct answer from the options given below:

If A is a square matrix of order 3 such that $|A| = 3$, then $|adj(adj A)|$ is equal to:

If $A = \begin{bmatrix}1 & -1\\2 & -1\end{bmatrix}, B = \begin{bmatrix}x & 1\\y & -1\end{bmatrix}$ and $(A+B)^2 = A^2 + B^2$, then which of the following are correct?

A. $x=1$

B. $x=4$

C. $y=1$

D. $y=4$

Choose the correct answer from the options given below:

If $A = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 0 & 2 \\ x & 1 & 1 \end{bmatrix}$ and $A^{-1} = \frac{1}{4}\begin{bmatrix} -2 & 0 & y \\ 5 & -2 & -1 \\ 1 & 2 & -1 \end{bmatrix}$, then values of x and y, are:

Let $A = \begin{bmatrix} 1 & -2 & 3 \\ 1 & 2 & 1 \\ \lambda & 2 & -3 \end{bmatrix}$. If $A^{-1}$ does not exist, then $\lambda =$

If $A = \begin{bmatrix}1 & 2\\2 & 1\end{bmatrix}$ and $f(x) = x^2-2x-3$, then $f(A)$ is

If $A$ is a square matrix of order $n \times n$, then which of the following are correct?

(A) $|kA| = k^n|A|$, $k$ is a constant

(B) $|k\ adjA| = k^n|adjA|^{n-1}$, $k$ is a constant

(C) $|adj\ adjA| = |A|^{(n-1)^2}$

(D) $A(adjA) = |A|I$, $I$ is an identity matrix of order $n$

Choose the correct answer from the options given below: